Problem Solving using Linear Systems

Question

The total cost of 15 gallons of regular unleaded gasoline and 10 gallons of premium unleaded gasoline is $35.50. Premium unleaded cost $0.20 more per gallon than regular unleaded. What is the cost per gallon of each type of gasoline?

Answer 1

Let's start by labeling premium and regular. premium = p, regular = r. so the first sentence is saying our equation 15r +10p = 35.50 then they tell us premium is $0.20 more per gallon than regular. we can write this as p = r + 0.2.

From this last equation we know p = r + 0.2 so we can substitute (r+ 0.2) in for "p" in the original equation. Giving us 35.50 = 15r + 10(r + 0.2) . we can use the Distributive Property to give us 35.50 = 15r +10r +10*0.2 and simplifying and combining like terms gives us 35.50 = 25r + 2 then we subtract the 2 from both sides leaving us with 33.50 = 25r and divide both sides by 25 giving us our amount for r which = $1.34 per gallon. then we replace that into the r in p = r + 0.2 giving us p = 1.34 + 0.2 = 1.54 so we have r = $1.34 per gallon and p = $1.54 per gallon

Answer 2

Let r = the cost regular and p = the cost of premium

15r + 10p = 35.50

p = r + .20

15r + 10(r+.2) = 35.50

15r + 10r + 2 = 35.50

25r = 35.50-2

r = 33.50/25 = 1.34

p = r+.2 = 1.54

Regular costs $1.34 per gallon and Premium costs $1.54 per gallon.